Some fruits are bought at 11 for ₹100 and twice the number at 8 for ₹100. If all the fruits are sold at 9 for ₹100, then what is the profit or loss percentage ?

Options

A. Gain 3
B. Loss, 3
C. Gain , `4(1)/(9)`
D. Loss, `2 (2)/(9)`

Answer

To solve the problem step by step, let's break it down clearly.

### Step 1: Determine the number of fruits bought at the first rate
- The first rate is 11 fruits for ₹100.
- Let’s denote the number of fruits bought at this rate as \( n \).
- Therefore, the cost for these fruits is:
\[ \text{Cost Price (CP1)} = \frac{100}{11} \times n \]

### Step 2: Determine the number of fruits bought at the second rate
- The second rate is twice the number of fruits bought at the first rate, which is \( 2n \).
- The rate for these fruits is 8 fruits for ₹100.
- Therefore, the cost for these fruits is:
\[ \text{Cost Price (CP2)} = \frac{100}{8} \times (2n) = \frac{200n}{8} = 25n \]

### Step 3: Calculate the total cost price of all fruits
- The total cost price (CP) for all fruits is:
\[ \text{Total Cost Price} = CP1 + CP2 = \frac{100n}{11} + 25n \]
- To combine these, we need a common denominator:
\[ \text{Total Cost Price} = \frac{100n}{11} + \frac{275n}{11} = \frac{375n}{11} \]

### Step 4: Calculate the total number of fruits
- The total number of fruits is:
\[ \text{Total Fruits} = n + 2n = 3n \]

### Step 5: Calculate the selling price of all fruits
- The selling price is given as 9 fruits for ₹100.
- Therefore, the selling price (SP) for all fruits is:
\[ \text{Selling Price} = \frac{100}{9} \times (3n) = \frac{300n}{9} = \frac{100n}{3} \]

### Step 6: Calculate profit or loss
- Profit or Loss is calculated as:
\[ \text{Profit or Loss} = \text{Selling Price} - \text{Total Cost Price} \]
- Substituting the values:
\[ \text{Profit or Loss} = \frac{100n}{3} - \frac{375n}{11} \]
- To combine these, we need a common denominator (which is 33):
\[ \text{Profit or Loss} = \frac{1100n}{33} - \frac{1125n}{33} = \frac{-25n}{33} \]
- This indicates a loss.

### Step 7: Calculate the loss percentage
- The loss percentage is calculated as:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Total Cost Price}} \right) \times 100 \]
- Substituting the values:
\[ \text{Loss Percentage} = \left( \frac{\frac{25n}{33}}{\frac{375n}{11}} \right) \times 100 \]
- Simplifying:
\[ = \left( \frac{25n \times 11}{375n \times 33} \right) \times 100 = \left( \frac{275}{12375} \right) \times 100 \]
- This simplifies to approximately 2.22%.

### Final Answer
The loss percentage is approximately **2.22%**.